This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A351049 #13 Apr 08 2025 11:09:11
%S A351049 1,1,1,4,16,67,307,1585,9235,59548,415564,3094807,24452785,204611653,
%T A351049 1810429597,16892405896,165592138372,1698918207403,18184602679435,
%U A351049 202577753111653,2344503929765023,28146188358379120,349996346545057288,4501360727764475503
%N A351049 G.f. A(x) satisfies: A(x) = 1 + x + x^2 * A(x/(1 - 3*x)) / (1 - 3*x).
%C A351049 Shifts 2 places left under 3rd-order binomial transform.
%H A351049 Seiichi Manyama, <a href="/A351049/b351049.txt">Table of n, a(n) for n = 0..540</a>
%F A351049 a(0) = a(1) = 1; a(n) = Sum_{k=0..n-2} binomial(n-2,k) * 3^k * a(n-k-2).
%t A351049 nmax = 23; A[_] = 0; Do[A[x_] = 1 + x + x^2 A[x/(1 - 3 x)]/(1 - 3 x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t A351049 a[0] = a[1] = 1; a[n_] := a[n] = Sum[Binomial[n - 2, k] 3^k a[n - k - 2], {k, 0, n - 2}]; Table[a[n], {n, 0, 23}]
%Y A351049 Cf. A004212, A007472, A007476, A351050.
%K A351049 nonn
%O A351049 0,4
%A A351049 _Ilya Gutkovskiy_, Jan 30 2022